Corpus ID: 119619691

# Order-Preserving Freiman Isomorphisms

@article{Amirkhanyan2018OrderPreservingFI,
title={Order-Preserving Freiman Isomorphisms},
author={G. Amirkhanyan and A. Bush and E. Croot},
journal={Integers},
year={2018},
volume={18},
pages={A8}
}
• Published 2018
• Mathematics, Computer Science
• Integers
• An order-preserving Freiman 2-isomorphism is a map $\phi:X \rightarrow \mathbb{R}$ such that $\phi(a) < \phi(b)$ if and only if $a < b$ and $\phi(a)+\phi(b) = \phi(c)+\phi(d)$ if and only if $a+b=c+d$ for any $a,b,c,d \in X$. We show that for any $A \subseteq \mathbb{Z}$, if $|A+A| \le K|A|$, then there exists a subset $A' \subseteq A$ such that the following holds: $|A'| \gg_K |A|$ and there exists an order-preserving Freiman 2-isomorphism \$\phi: A' \rightarrow [-c|A|,c|A|] \cap \mathbb{Z… CONTINUE READING

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